Line the bottom of a 13 by 9 by 2-inch dish with 1 bag of cookies and layer bananas on top.
In a bowl, combine the milk and pudding mix and blend well using a handheld electric mixer. Using another bowl, combine the cream cheese and condensed milk together and mix until smooth. Fold the whipped topping into the cream cheese mixture. Add the cream cheese mixture to the pudding mixture and stir until well blended.
Pour 1/2 of pudding mixture over the bananas. Next, lay the second bag of cookies over the pudding and layer with bananas and the rest of the pudding mixture. Cover with remaining bag of cookies. Refrigerate until ready to serve.